Coupling of evanescent and propagating guided modes in locally resonant phononic crystals

In this paper, we present a combined theoretical, numerical and experimental study of acoustic wave propagation in 1D locally resonant phononic crystals made of acoustic resonators grafted onto a waveguide. The case of one single resonator grafted onto the waveguide is first investigated and a model of transmission cancellation at resonant frequencies is obtained. The model includes the excitation of evanescent guided waves attached to the grafting points. When extended to periodical arrays of grafted resonators, the model provides us with a definite theoretical expression for the complex band structure. Comparison with experimental results and complex band structures obtained by numerical simulation suggests a strong dependence of transmission through the crystal on the lattice constant of the grafted resonators. It is found that evanescent waves in the waveguide play a key role when the lattice constant is in the sub-wavelength range.